Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259344 | C2 | semidirect |
| 2. C2×#20259342 | C2 | semidirect |
| 3. #27133209 | C2 | semidirect |
| 4. #27133056 | C2 | semidirect |
| 5. #27133054 | C2 | semidirect |
| 6. #27133051 | C2 | semidirect |
| 7. #27133049 | C2 | semidirect |
| 8. C2×#20259232 | C2 | semidirect |
| 9. C2×#135×C191 | C2 | semidirect |
| 51. C2×C191⋊C8 | D4 | semidirect |
| 68. C2×C8×C191 | D4 | semidirect |
| 116. C191 | #3150 | semidirect |
| 120. C2×#135 | D191 | semidirect |
| 180. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259344 | 2 |
| C2×#20259342 | 2 |
| #27133209 | 2 |
| #27133056 | 2 |
| #27133054 | 2 |
| #27133051 | 2 |
| #27133049 | 2 |
| C2×#20259232 | 2 |
| C2×#135×C191 | 2 |
| #3150 | 191 |